(-5n-7)(n+8)=0

Solution for (-5n-7)(n+8)=0 equation:

(-5n-7)(n+8)=0

We multiply parentheses ..

(-5n^2-40n-7n-56)=0

We get rid of parentheses

-5n^2-40n-7n-56=0

We add all the numbers together, and all the variables

-5n^2-47n-56=0

a = -5; b = -47; c = -56;
Δ = b2-4ac
Δ = -472-4·(-5)·(-56)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-33}{2*-5}=\frac{14}{-10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+33}{2*-5}=\frac{80}{-10}
=-8
$